Domino phase retrieval algorithm for structure determination using electron diffraction and high resolution transmission electron microscopy patterns

Abstract

Direct method formalism to determine atomic structures using the electron diffraction data is here aimed at a general solution of the phase retrieval problem, consequently combining the electron diffraction (ED) and the high-resolution transmission electron microscopy (HRTEM) patterns in a "domino" fashion. While there are similarities to what there is in conventional (kinematical) direct methods, there remain major differences, in particular, owing to the dynamical effects in the data the ED structure factors prove to be complex and then, the positivity of the reconstructed electron density is no longer a valid constraint for 'dynamical' direct methods. Besides, due to the dynamical effects heavy atoms need not dominantly contribute the HRTEM images any more. Thus, the 'dynamical' direct methods concept has to base upon it that the phase retrieval algorithm will utilize both the dynamical ED and HRTEM data. Noteworthy is the fact that the fusion of the traditional direct method technique, which is described here, allows to realize a full phase restoration of complex structure factors. The numerical example, using the dynamical ED and HRTEM data for (Ga,In)₂SnO₅5 ceramic, shows that the method is capable of yielding unique phase retrieval solution. The clear sense is that the domino transform algorithm proposed works well and represents a valuable method for phasing diffraction patterns in electron structural crystallography using an experiment, which is readily to perform within collecting the ED and HRTEM data.